Once you have calculated the standard deviation for your data, a legitimate
question to ask is "How reliable is the calculated standard deviation?".
For this situation the Chi Squared distribution can be used to calculate
confidence intervals for the standard deviation.

and then loop over the values of alpha and calculate the intervals for
each: remember that the lower critical value is the same as the quantile,
and the upper critical value is the same as the quantile from the complement
of the probability:

Similarly, we can also list the confidence intervals for the standard
deviation for the common confidence levels 95%, for increasing numbers
of observations.

The standard deviation used to compute these values is unity, so the
limits listed are multipliers for any
particular standard deviation. For example, given a standard deviation
of 0.0062789 as in the example above; for 100 observations the multiplier
is 0.8780 giving the lower confidence limit of 0.8780 * 0.006728 = 0.00551.

With just 2 observations the limits are from 0.445
up to to 31.9, so the standard deviation
might be about half the observed value
up to 30 times the observed value!

Estimating a standard deviation with just a handful of values leaves
a very great uncertainty, especially the upper limit. Note especially
how far the upper limit is skewed from the most likely standard deviation.

Even for 10 observations, normally considered a reasonable number, the
range is still from 0.69 to 1.8, about a range of 0.7 to 2, and is still
highly skewed with an upper limit twice
the median.

When we have 1000 observations, the estimate of the standard deviation
is starting to look convincing, with a range from 0.95 to 1.05 - now
near symmetrical, but still about + or - 5%.

Only when we have 10000 or more repeated observations can we start to
be reasonably confident (provided we are sure that other factors like
drift are not creeping in).

For 10000 observations, the interval is 0.99 to 1.1 - finally a really
convincing + or -1% confidence.